What Is Hypothesis Test P-Value?
A p-value is the probability of getting a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. A small p-value, below your chosen α, is evidence against the null hypothesis.
Pick the distribution of your statistic, enter its value and degrees of freedom, choose the tail, and the calculator returns the p-value, the critical value, the left and right areas and the reject or fail-to-reject decision, with the p-value shaded on the curve.
The sections below explain the formulas, variables, a worked t-test example and answers to common questions about tails and what a p-value does and does not mean.
How to Use the Hypothesis Test P-Value Calculator
- Pick the type of test statistic: z, t, χ² or F.
- Enter the statistic and its degrees of freedom.
- Choose one- or two-tailed and your α.
- Read the p-value, critical value and decision.
Hypothesis Test P-Value Formula
Right-tailed p-value
Left-tailed p-value
Two-tailed p-value (z, t)
Hypothesis Test P-Value Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| s | Observed test statistic | z, t, χ² or F |
| df | Degrees of freedom | not needed for z |
| α | Significance level | commonly 0.05 |
| p | p-value | tail area beyond s |
Hypothesis Test P-Value Worked Example
A two-tailed t-test gives t = 2.31 with 24 degrees of freedom. The right-tail area beyond 2.31 is about 0.0148, so p ≈ 2 × 0.0148 = 0.0297. At α = 0.05 this is significant (0.0297 < 0.05), but at α = 0.01 it would not be.
With the example values loaded in the calculator above, the steps are:
- Test statistic t = 2.31, df = 24.
- Left area = 0.98509938; right area = 0.01490062.
- Two-tailed p = 2 × the smaller tail area (for the symmetric z and t distributions).
- Compare p = 0.0298012 with α = 0.05: p < α, so reject H₀.
Result: p-value = 0.0298012; Decision at α = Reject H₀ (p < 0.05).
Where Hypothesis Test P-Value Is Used
Hypothesis tests
Finding p after computing a t, z, χ² or F statistic by hand.
Checking software output
Verifying a p-value reported for a test statistic.
Exams and coursework
Replacing table look-ups with exact values.
Choosing tails
Comparing one- and two-tailed p-values.
Common Hypothesis Test P-Value Mistakes to Avoid
- Choose α before looking at the data.
- Use the same tail as your alternative hypothesis.
- Report the exact p-value, not just "p < 0.05".
Hypothesis Test P-Value Terms and Definitions
- p-value
- The probability, assuming H₀ is true, of a statistic at least as extreme as observed.
- Critical value
- The cut-off statistic where p equals α.
Hypothesis Test P-Value FAQs
How do I find the p-value from a test statistic?
Find the area in the tail(s) of the statistic's distribution beyond the observed value.
What is the p-value for z = 1.96?
About 0.05 for a two-tailed test and 0.025 for a one-tailed test.
What does p < 0.05 mean?
The result would be unusual if H₀ were true, so it is called statistically significant at the 5% level.
Why is a two-tailed p-value double a one-tailed one?
Because both tails count as extreme, for the symmetric z and t distributions.